Yes and no. Mostly I haven’t had a problem with USB-C cable orientation but I think once or twice connecting random devices I have had the problem. I am not necessarily talking about charging.
Bottom line: If a random peripheral isn’t working, it’s worth rotating the cable to see whether it changes anything.
It could be but it could be a firmware issue in the other end, in which case there’s not much you can do about it (other than rotate the cable).
Possible. I doubt it, given that you have a much more recent device.
USB PD firmware can be checked with: sudo cat /sys/kernel/debug/tps6598x/0-003f/customer_use
If you get 0x4c35445000000200 then I believe you have the latest.
However you won’t be able to check this now, I gather.